acta mechanica et automatica, vol.6 no.3 (2012)
APPLICABILITY OF INDICATORS OF TRABECULAR BONE STRUCTURE
FOR EVALUATION OF ITS MECHANICAL PROPERTIES
Artur CICHAŃSKI*, Krzysztof NOWICKI*, Adam MAZURKIEWICZ*, Tomasz TOPOLIŃSKI*
*Faculty of Mechanical Engineering, University of Technology and Life Sciences,
ul. Kaliskiego 7, 85-789 Bydgoszcz, Poland
[email protected], [email protected], [email protected], [email protected]
Abstract: The paper presents the results of examination of relations between indicators describing trabecular bone structure and its static
and cyclic compressive strength. Samples of human trabecular bone were subject to microtomographic tests in order to specify indicators
describing its structure. Part of the samples was subject to static compression tests, part to cyclic compressing loads with stepwise increasing amplitude. Evaluation of a degree of applicability level of estimation of bone compressive strength properties was conducted based upon
values of structure indicators. Evaluation was performed based upon values of obtained determination coefficients R2 for linear regression.
Obtained R2 values were within the range of 0.30-0.51 for relations between examined indicators and static compressive strength within
the range of 0.47-0.69 for relations with the results of cyclic test with stepwise increasing amplitude.
Key words: Trabecular Bone, Testing Method, Bone Structure Indicators
1. INTRODUCTION
Structure of human bone is subject to constant changes depending on various factors e.g. human activity, type of work performed etc. After 20-30 year of age a process of decreasing
of bone mass commences. It results in the change of bone structure describing indicators and decrease of compressive strength
properties of bone tissue (Biewener, 1993; Taylor and Tanner,
1997; Warden et al., 2006). If, with age diseases impairing bone
metabolism occur, such as e.g. osteoporosis, dynamics of such
changes increases (Rapillard et al., 2006).
Typical bone load is the compressing load applied to e.g. long
bones of lower limbs or spine. It is a cyclic load e.g. during walking, thus behaviour under such load is the fatigue behavior (Warden et al., 2006; Keaveny et al., 1993; Martin, 2003).
The target of the hereby paper is to specify applicability of indicators describing trabecular bone structure for the description
of its compressive strength properties specified in static compression test and cyclic compression test under loads with stepwiseincreasing amplitude.
2. MATERIAL AND METHODS
For static tests 42 and for cyclic tests 62 samples of human
trabecular bone were used, taken from human femur head. The
samples were not divided into sub-groups acc. To e.g. age, sex,
type of disease or any other factors. Preparations the samples
were made of were obtained as a result of implantation of femoral
joint.
Samples were in the shape of a cylinder of diameter of 10mm
and height of 8.5mm. Sample taking manner is presented
on Fig. 1. A slice of 8.5mm thickness was cut from the head base
perpendicularly to neck axis, then a cylinder of 10mm diameter
and 8.5mm height was cut from central part of the slice.
Fig. 1. Manner of taking samples for tests
All samples were tested at micro-tomograph µCT80 at separation of 36µm between subsequent scans for the following parameters: 70kV, 114µA, 500 projections/180°, and 300ms integration time. Upon scanning, as standard, values of 5 bone structure
indicators were obtained: average constant trabecular number per
sample volume – Trabecular Number Tb.N, average trabecular
thickness in a sample – Trabecular Thickness Tb.Th, average
trabecular separation in a sample - Trabecular Separation Tb.Sp,
quotient of tissue volume vs. volume of the whole sample – Bone
Volume Fraction BV/TV, and quotient of tissue surface field
in a sample vs. its volume – Bone Surface Ratio BS/BV (Parfitt
et al., 1987).
27
Artur Cichański, Krzysztof Nowicki, Adam Mazurkiewicz, Tomasz Topoliński
Applicability of Indicators of Trabecular Bone Structure for Evaluation of its Mechanical Properties
Static compression test was made on strength testing machine MiniBionix 858. The test defined compression strength
of samples indicated as US (Ultimate Strength).
In the first part of a test five cycles of loading and relieving
for deformation value from ε=0 to ε=0.8% were performed. Initial
load, for which ε=0 was assumed, was specified as 50N. Intervals
between cycles were five seconds. The cycles were made
to stabilize contact surfaces of sample-machine. Test program
is presented at Fig. 2.
At the next stage the test was performed until obtaining
of compression strength value i.e. obtaining the first maximum
at compression curve. From the specified curve compression
strength value US was calculated, i.e. stress value at the first
curve maximum point.
Static test was performed at room ambient temperature.
solution of NaCl at temperature of 37±2°C.
3. TEST RESULTS
Tables 1-2 present ranges, average values and standard deviations, relative RSD values of structure indicators obtained from
microtomographic tests for groups of samples subject to static
compression and cyclic test. Tab. 3 presents analogical values
achieved for US compressive strength and fatigue life N obtained
in static compression test and in cyclic test with stepwise increasing load.
Tab. 1. Ranges, average values and standard deviations relative values
of structure indicators obtained from microtomographic tests
for samples subject to static compression
BS/BV, BV/TV,
Tb.N, 1/mm Tb.Th, mm Tb.Sp, mm
1/mm
Min.
7.737
Max. 22.505
Average 13.903
RSD, %
22
0.068
0.392
0.222
36
0.76
1.958
1.436
19
0.089
0.259
0.151
24
0.331
1.223
0.572
32
Tab. 2. Ranges, average values and standard deviations relative values
of structure indicators obtained from microtomographic tests
for samples subject to cyclic test
Fig. 2. Static compression test program
Min.
Max.
Average
RSD, %
BS/BV,
1/mm
BV/TV,
-
Tb.N,
1/mm
Tb.Th,
mm
Tb.Sp,
mm
5.206
18.995
11.998
23
0.066
0.459
0.204
37
0.511
1.543
1.1329
20
0.105
0.384
0.176
26
0.424
1.829
0.749
34
Tab. 3. Ranges, average values and standard deviations relative values
of US compressive strength and fatigue life N, obtained in static
compression test and cyclic test with stepwise increasing load
Fig. 3. Cyclic test with stepwise increasing amplitude program
Cyclic tests of bone samples were performed in the conditions
of compression upon stepwise increasing load at strength testing
machine INSTRON 8874. Frequency of changes of sinusoidal
load was 1 Hz. Minimum load for all load levels was 5N. Maximum
load started at 20N with 10N increments at subsequent stages.
Volume of stages is 500 cycles realized in fixed amplitude conditions. The test program is presented at Fig. 3. During every tests
10 cycles recording of sample load and deformations was made
with 100 Hz sampling. Measuring signal from strength testing
machine processed with low-pass filter cutting off frequencies
exceeding 10Hz in order to equalize current interferences
and the noise of measuring devices (dynamometer).
In order to identify fatigue life median of values of deformations increments was specified; then, the first loop, was identified as the value of fatigue life N, for which deformation increment
exceeded the value of the specified median by 10%.
Cyclic tests were performed in controlled environment – 0.9%
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Min.
Max.
Average
RSD
US, MPa
1.678
36.143
12.675
55%
N, number of cycles
9.75—103
3.52—104
20.73—103
55%
Tab. 4. Values of R2 determination coefficients for relations between
bone structure indicators and its static compressive strength
and cyclic strength
Indicator
Static compressive
strength US, MPa
Fatigue life N,
number of cycles
BS/BV, 1/mm
0.44
0.50
BV/TV, Tb.N, 1/mm
0.51
0.30
0.69
0.50
Tb.Sp, mm
Tb.Th, mm
0.36
0.48
0.47
0.50
Tab. 4 presents values of R2 determination coefficients, obtained with application of linear regression for relations between
acta mechanica et automatica, vol.6 no.3 (2012)
0,3
0,25
Tb.Th, mm
bone structure indicators and its static compressive strength
and fatigue life.
Figs. 4-5 present dependencies between BV/TV and Tb.Th
and static compressive strength US
Figs. 6-7, on the other hand, present dependencies between
BV/TV and Tb.Th and fatigue life obtained during the test
with stepwise increasing amplitude.
0,2
0,15
0,1
y = 2E-06x + 0,1231
R2 = 0,5028
0,05
30
0
25
0
US, MPa
40000
60000
15
Fatigue life, N
Fig. 7. Relation between Tb.Th value and fatigue life
obtained during the test with stepwise increasing amplitude
10
4. DISCUSION
20
y = 52,979x - 1,5746
5
R2 = 0,5112
0
0
0,1
0,2
0,3
0,4
0,5
BV/TV, Fig. 4. Relation between BV/TV and static compressive strength US
30
y = 113,09x - 6,9245
R 2 = 0,4804
25
US, MPa
20000
20
15
10
5
0
0
0,1
0,2
0,3
Tb.Th, mm
Fig. 5. Relation between Tb.Th value
and static compressive strength US
0,5
Performed tests refer to samples from over 100 donors thus
on relatively big population. Usually (Rapillard at al., 2006; Haddock et al., 2004; Zioupos et al., 2008) tests refer to no more than
10 donors and the samples are multiplied by taking of more than a
single sample from each donor. Thus, we are dealing with significant variability of sample structures resulting from individual properties and pathological properties (osteoporosis, coxarthrosis).
If the structure was described with variability of relative BV / TV
volume coefficient, it would be 36-37%, which is close to maximum values of variability quoted in literature (Haddock et al.,
2004). Both performed tests are statistically homogenous – examined relative structure indicators differ maximally by 2%.
The measure of strength of connection of two independent
factors in functional description of regression is R2 determination
coefficient. Referring the results obtained from structure tests
for first group to static compressive strength determination coefficient R2 for tested indicators was specified up to the value of 0.5 –
the highest value for BV/TV. For the second group the same
value, but for fatigue life, is 0.69 which can be considered high for
this variability. Also, for all other structure indicators with respect
to fatigue life, determination coefficient value is significantly higher. It indicates that examinations of bone fracture risk testing
method with stepwise increasing amplitude allows for obtaining
better correlation with bone structure, in particular with BV/TV
indicator.
REFERENCES
BV/TV, -
0,4
0,3
0,2
y = 6E-06x + 0,0895
0,1
R 2 = 0,689
0
0
20000
40000
60000
Fatigue life, N
Fig. 6. Relation between BV/TV value and fatigue life
obtained during the test with stepwise increasing amplitude
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29
Artur Cichański, Krzysztof Nowicki, Adam Mazurkiewicz, Tomasz Topoliński
Applicability of Indicators of Trabecular Bone Structure for Evaluation of its Mechanical Properties
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Acknowledgement: This work by supported by The State Committee
for Scientific Research (KBN) under grant No. N N501 308934.
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